How do I match the UV map with the image used as texture
you can manually reposition the vertices of the UV map so that it matches with the mesh.

Select a vertex, press L to select all of the linked vertices and use the regular tools to edit, grab, size, rotate, etc.







As an alternative you can export the UV map as image and use it as reference to position the image so that it matches the UVs in an image editing app, then re-import the image and it should match the geometry.